What is the equation of a circle with a center at (-4,0) that passes through the point (-2,1)

The  equation of a circle with a center at (-4,0) that passes through the point (-2,1) is x² + y² + 2x - 2y =0

Step-by-step explanation:

It is given that,

a circle with center at (-4,0) that passes through the point (-2,1)

To find the radius of circle.

Radius r = √[(-2 --4)² + (1-0)²]

r = √[(-2 +4)² + 1²]

= √[2² + 1²] = √(4 + 1)  =√5

To find the equation of circle

(x - -2)² + (y - 1)² = (√5)²

(x + 2)² + (y - 1)² = 5

x² + 2x + 4 + y² -2y +1 = 5

x² + y² + 2x - 2y + 5 = 5

x² + y² + 2x - 2y =0